Preheat oven to 350 degrees F.
In a food processor finely grind almonds with confectioners' sugar and transfer to a large bowl. In food processor pulse butter with flour until mixture resembles fine crumbs and add to almond mixture with cornstarch and salt, stirring until combined well.
In a small bowl beat together egg and lemon juice until blended and stir into flour mixture until combined well. Work mixture with hands until it forms a dough.
Pat 1 1/2 cups dough into a disk and chill, wrapped in plastic wrap, 20 minutes. Pat remaining dough evenly into a 17 1/2 by 11-inch jelly-roll pan and spread evenly with jam.
On a lightly floured surface with a floured rolling pin roll out chilled dough 1/8 inch thick and with a 3/4 to 1 1/2-inch star-shaped cookie cutter (we used 3 different sizes) cut out as many stars as possible. Re-roll scraps and cut out more stars. Arrange stars randomly over jam and carefully brush stars with milk. Sprinkle stars with granulated sugar and bake in middle of oven 30 minutes, or until stars are golden. Cool confection in pan on a rack and cut into 20 bars.